I want to point one thing out, I think whether or not you check out the original is also dependent on how much you like the cover.
For instance, I quite like Metallica's Garage Inc. But did I check out the original of every one of those songs? Nah.
I really liked Turn the Page, Whiskey in the Jar, Tuesday's Gone, and Sabbra Caddabra, so I checked out the originals of all of those (well.......as close as I could get to an original for Whiskey in the Jar). But the rest? I just didn't care enough. I wasn't AMAZINGLY into any of the other covers, so I didn't feel the need to check out the original.
Like when Alien Ant Farm did that cover of Smooth Criminal. I didn't check out the original for a very long time. Why? Because I passively liked the cover, I didn't love it and definietely didn't care about the song enough to find its most "pure" form. Nothing to do with how old it was, just didn't care that much about the song, even if I liked it.